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The Dichotomy of Forms and Operators and the Role of Green’s Forms

In: Trails in Modern Theoretical and Mathematical Physics

Author

Listed:
  • Bernhelm Booß-Bavnbek

    (Roskilde University, Department of Sciences and Environment)

  • Yihan Ji

    (Nankai University, Chern Institute of Mathematics and Laboratory of Pure Mathematics and Combinatorics (LPMC))

  • Alessandro Portaluri

    (Università degli studi di Torino, Dipartimento di Scienze Agrarie, Forestali e Alimentari - DISAFA)

  • Chaofeng Zhu

    (Nankai University, Chern Institute of Mathematics and Laboratory of Pure Mathematics and Combinatorics (LPMC))

Abstract

We consider a sesquilinear form on sections of a Hermitian bundle over a (not necessarily compact) smooth Riemannian manifold with boundary. We assume that in local coordinates, the form can be written as the integral of the inner product of differential expressions of the sections. We assign a linear operator to the form and show that it is a uniquely determined differential operator. We prove the existence and uniqueness of a differential operator on the boundary which makes a variant of Green’s formula hold.

Suggested Citation

  • Bernhelm Booß-Bavnbek & Yihan Ji & Alessandro Portaluri & Chaofeng Zhu, 2023. "The Dichotomy of Forms and Operators and the Role of Green’s Forms," Springer Books, in: Andrea Cintio & Alessandro Michelangeli (ed.), Trails in Modern Theoretical and Mathematical Physics, pages 53-70, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-44988-8_5
    DOI: 10.1007/978-3-031-44988-8_5
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